A Battery-Aware Deployment Scheme for Cooperative Wireless Sensor Networks Jiucai Zhang, Song Ci, Hamid Sharif, and Mahmoud Alahmad∗ Department of Computer and Electronics Engineering University of Nebraska-Lincoln, NE 68182, USA ∗ Department of Architecture Engineering University of Nebraska-Lincoln, NE 68182, USA
[email protected], {sci2, hsharif, malahmad2}@unl.edu Abstract—Although current research focused on sensor deployment to balance the energy consumption among the sensor nodes for prolonging the lifetime of wireless sensor networks, sensor nodes with larger communication radius have to consume more energy to overcome wireless channel fading and path loss. Cooperative transmission allows nodes with single-antenna to cooperate on information transmission and/or reception to achieve a lower average error probability than its non-cooperative counterpart under the same transmit energy budge. In this work, we introduce the concept of cooperative transmission into sensor deployment to balance the energy consumption among sensor nodes. The key idea is to deploy an optimal number of cooperative nodes into a given area. In this way, batteries of all sensor nodes are discharged at the same rate. Extensive simulations have been conducted to evaluate the performance of the proposed scheme. Compared with non-cooperative cases, the proposed scheme with cooperative transmission improves the battery energy efficiency by 52.1%, and prolongs the lifetime of wireless sensor network by three times.
Fig. 1.
Demonstration of cooperative transmission
I. I NTRODUCTION With the rapid development of computing hardware, more and more functions have been integrated into a wireless sensor node, yet its size has been decreased greatly. Such wireless sensor nodes are typically powered by batteries. Replacement of these batteries is challenging and expensive due to the large quantity of the sensor nodes or special applications like battle field surveillance. Consequently, maximizing the lifetime of wireless sensor networks is a critical design consideration. In general, the lifetime of a wireless sensor network is greatly affected by channel fading, which requires more transmit energy to guarantee a given packet error rate. Furthermore, unequal communication load distribution causes the nodes closer to the sink consumed more energy, which depletes their batteries faster, and thus severely shortens the network lifetime. Cooperative transmission takes advantage of the spatial diversity to enhance the channel throughput under fading by allowing single-antenna nodes to cooperate on information transmission and/or reception as shown in Figure 1. The cooperated nodes interact with each other to jointly transmit the information from the source to the destination [1]. The source (S1 ) intends transmit data to the destination (Sink) via relay nodes. The data will firstly be transmitted to relay nodes R1 , R2 , and R3 ), then cooperative transmission will be used to forward the data to its final destination (Sink). Without
losing generality, in this paper a network protocol is assumed to be adopted to select the optimal relay nodes and conduct the multihop routing [2] in a given sensor network. For the same throughput requirement, cooperative transmission requires much less transmission energy than noncooperative systems [3], [4]. In [4], cooperative MIMO transmission and reception can simultaneously achieve both energy savings and delay reduction. In [5], cooperative transmission has been adopted to reduce the portion of transmit energy in total energy consumption, and helped to reduce the energy difference among sensor nodes. On the other hand, energy-aware sensor deployment is an effective way to balance the energy consumption among sensor nodes. In our previous work [6], optimal communication radii were assigned to different rings in a circular network topology to keep an even energy consumption throughout the entire network. However, in that work, the communication radius of the outermost ring tends to be large, which will reduce the lifetime of the wireless sensor network. In this paper, we introduce the cooperative transmission into the previous wireless sensor network deployment to reduce the energy consumption caused by channel fading. Specifically, an optimal number of cooperative nodes will be chosen for each ring of the network topology to further reduce the energy consumption. Extensive simulations have been conducted to evaluate the performance
978-1-4244-4148-8/09/$25.00 ©2009 This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE "GLOBECOM" 2009 proceedings.
1 Normalized Available Capacity
of the proposed deployment scheme. Compared with the noncooperative case in [6], cooperative transmission can reduce energy consumption at all sensor nodes. The battery utilization can be improved by about 52.1%, and the lifetime of network can be improved by three times. The rest of the paper is organized as follows. In Section II, we introduce battery model and power consumption model of a sensor node. Cooperative transmission in wireless sensor networks is discussed in Section III. We analyze lifetime optimization by applying the cooperative transmission into the sensor deployment in Section IV. We discuss the simulation results in Section V and give concluding remarks in Section VI.
0.95
0.9
0.85
Non−cooperation 2 cooperation nodes 3 cooperation nodes 4 cooperation nodes 5 cooperation nodes
0.8 0
II. S YSTEM M ODELS
50 100 150 Communication Radius (m)
A. Battery Model Available battery capacity has a nonlinear relationship with its discharging current. A battery tends to provide more energy at a lower discharge current, which is called battery current effect. To capture current effect, an analytical model in [7] is adopted in this work. When a battery is discharge at current rate of I in the time period [ts , te ], available capacity α(I, L, ts , te , β 2 ) can be denoted as follows: α(I, L, ts , te , β 2 ) = C0 − IF (L, ts , te , β 2 )
(1)
where, F (L, ts , te , β 2 ) = (ts − te ) ∞ −β2 i2 (L−ts ) −e−β2 i2 (L−te ) + 2 i=1 e β 2 i2 C0 is the full capacity. β is a constant related to the diffusion rate of the battery, whose value can be determined by data fitting [8]. i is a factor ranging from 1 to ∞. L is the total lifetime of the battery. The available capacity α(I, L, ts , te , β 2 ) is expressed in Coulombs, and is determined by two terms. The first term is the consumed capacity by the given load I. The second term is the capacity loss due to the current effect. B. Power Consumption Model of a Sensor Node The total average power consumption Pat of a sensor node along the signal path can be divided into two main components: the power consumption of all amplifiers PA and the power consumption of all other circuits PC [4], which is, (2)
The power consumed by amplifiers depends on the transmission power Pt , which can be approximated as: PA = (1 + η)Pt
(3)
where, η relies on the modulation scheme and the associated constellation size [4]. Pt can be calculated according to the link budget relationship [4], which can be denoted as: (4π)2 (4) Ml Nf × dk Gt Gr λ2 where, Eb is the required energy per bit at the receiver for a given BER. Rb is the bit rate. d is the distance between Pt (d) = Eb Rb
The normalized available capacity vs. communication radius
transmitter and receiver. k is the path loss factor. Gr and Gt are the gains of receiving and transmitting antennas respectively. λ is the wavelength of the carrier signal. Ml is the link margin. Nf is the receiving noise figure defined as Nf = Nr /N0 , where Nr is the total effective noise at the receiver input, and N0 denotes the single sided thermal noise power spectral density (PSD). Assuming the average power consumption of circuits for transmission is Pct , the total power consumption for the transmission Pat can be obtained as Pat (d) = Pt (d) + Pct
2
Pat = PA + PC .
Fig. 2.
200
(5)
To receive a data packet, only the receiver is involved, and its average power consumption is assumed as Pcr . Therefore, the average power consumption of a relay node with bit rate Rb is Ptotal = Pat (d) + Pcr
(6)
III. C OOPERATIVE T RANSMISSION IN W IRELESS S ENSOR N ETWORKS Cooperative transmission requires less transmission power under the same BER and throughput requirements. However, since cooperative transmission needs much more electronic circuits, it is not always energy-efficient [1]. It is only beneficial when the power saved by cooperative transmissions is more than the power dissipated by the additional involved circuits. The normalized available capacity versus communication radius is shown in Figure 2. Here, the available capacity of a battery at communication radius 0 with noncooperative transmission is assumed to be 1. We can observe that the optimal number of cooperative sensor nodes varies with the communication radius . Direct transmission is optimal within shorter communication radii, while the cooperative transmission is preferred for larger communication radii. Figure 3 shows that the optimal number of cooperative nodes over various communication radii. Thus, we can vary the number of cooperative nodes for a given communication radius to minimize the power consumption of sensor nodes.
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Therefore, each node has an average battery operating time:
Optimal Number of Cooperation Nodes
5 4.5
Lm =
4
=
ξm Im C0 Im
=
ϕV C0 Ptm (Jm ,dm )
3.5 3 2.5
−2
∞ i=1
e−β
−2
2 i2 (L −t ) 2 2 m s −e−β i (Lm −te ) β 2 i2 2 2 2 2 ∞ e−β i (Lm −ts ) −e−β i (Lm −te ) 2 2 i=1 β i
(10)
B. Sensing Model
2
To operate a wireless sensor network successfully, sensors nodes must maintain sensing coverage and network connectivity. According to [9], [10], the relationship between the communication range and the minimum number of node N2 needed to cover a ring belt A (R1 < r < R2) with a probability of at least 1 − σ can be obtained as:
1.5 1 0.5 0 0
50
100 150 Transmission Distance (m)
200
Fig. 3. Optimal number of cooperative nodes vs. communication radius. Here, vertical lines denote the transition points of optimal number of cooperative nodes.
N2 N log( σ2 )
≥
R22 −R12 (R2 −R1 )2
(11)
C. Network Models TABLE I S YSTEM PARAMETERS
Pb Gt Gr Rb Ml
10−3 0.5dBi 20kbps 40dB
Nf fc Pct K
10dB 2.5Ghz 98.2mW 2.5
N0 2
η Pcr R
174dBm/Hz 1.47 112.6mW 0.5
All system parameters adopted by this work are listed in Table I. A. Power Consumption Model for Cooperative Transmission Since the energy consumption in the sleep and the transient mode is much less than that in the active mode [4], the power consumption in these modes can be neglected. Assume that the STBS code [5] is used with code rate R, the power consumption of J cooperative relay nodes can be denoted as [5]: Pc (J, d) = Rb
(1+η)JEbcoop (J) Ml Nf dk RGt Gr λ2
+ J PRct + Pcr (7)
0 where, Ebcoop (J) = N1/J , and Pb is the required BER [3]. Pb The current needed to power a sensor node can be obtained as:
I=
Pc (J,d) φV
=
Rb
(1+η)JPbcoop (J) Pct Ml Nf dk +J R RGt Gr λ2
φV
+Pcr
(8)
where, V and φ denotes the DC-DC converter output voltage and efficiency respectively. Based on the battery model, the available capacity ξ of the battery of J cooperative sensor nodes with full capacity C0 and communication radius d can be denoted as 2 2 2 2 ∞ e−β i (L−ts ) − e−β i (L−te ) ξ = C0 − 2I (9) β 2 i2 i=1
In this work, sensor nodes are assumed to be evenly deployed in M concentric ring belts [6]. The sequence number of rings starts from the innermost to the outermost, i.e., the innermost is the 1st ring, and the outermost is the M th ring. The mth (m = 0, 1, · · · , M ) ring has Nm equally spaced array nodes, whose communication radius is denoted as Rm . Therefore, the number of nodes Km residing outside the ring m is: M (12) Km = Ni i=m+1
Thus, the average number of packet Nm relayed by a typical node in ring m is: M Ni (13) am = i=m+1 Nm So, the total power Ptm (Jm , Rm ) consumed by Jm cooperative transmission sensor nodes in the mth ring over distance Rm can be written as: ⎧ ⎨ (am + Jm )Pc (Jm , Rm − Rm−1 − Jm Pcr , 1 ≤ m < M(14) Ptm (Jm , Rm ) = ⎩ Jm Pc (Jm , Rm − Rm−1 ), m = M IV. L IFETIME O PTIMIZATION FOR W IRELESS S ENSOR N ETWORKS U SING THE C OOPERATIVE T RANSMISSION To balance the power consumption among the sensor nodes, the average operating time of each sensor nodes should be equal. L = L1 = L2 = · · · LM
(15)
Thus, the problem turns into determining the numbers of node Nm , the communication range Rm , and number of cooperative nodes Jm for mth ring, which can be formulated as follows: MaximizeL = Lm ,
m = 1, 2, · · · , M
(16)
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TABLE II S IMULATION PARAMETERS
Subject to: ⎧ R2 −R2 Nm ⎪ ⎪ ≥ (R m−R m−1)2 Nm ⎪ log( ) m ⎪ m−1 σ ⎪ ⎪ ∞ e−β2 i2 (L1 −ts ) −e−β2 i2 (L1 −te ) ⎪ ϕV C0 ⎪ = ⎨ Pt1 (J1 ,d1 ) − 2 i=1 β 2 i2 ∞ e−β2 i2 (L2 −ts ) −e−β2 i2 (L2 −te ) (17) ϕV C0 = ⎪ i=1 Pt2 (J2 ,d2 ) − 2 β 2 i2 ⎪ ⎪ ⎪ ,..., = ⎪ ⎪ ⎪ ∞ e−β2 i2 (LM −ts ) −e−β2 i2 (LM −te ) ⎪ ϕV C0 ⎩ i=1 PtM (JM ,dM ) − 2 β 2 i2
R σ φ V
λj φj (R, N )
(18)
j=1
where, λ1 , λ2 , . . . ,λM are the Lagrangian multipliers, and ϕj is the equation constructed as: ϕj
=
ϕj+M = =
Nj
N log( σj
−
2 Rj2 −Rj−1 (Rj −Rj−1 )2 ,
j = 1, 2, ...M
) φV C0 Ptj+1 (Jj+1 ,dj+1 ) ∞ −β2 i2 (Lj+1 −ts ) −e−β2 i2 (Lj+1 −te ) (19) − 2 i=1 e β 2 i2 ∞ e−β2 i2 (Lj −ts ) −e−β2 i2 (Lj −te ) φV C0 i=1 Ptj (Jj ,dj ) − 2 β 2 i2
The values of λ1 , λ2 , . . . , λM , the maximum lifetime L, the numbers of cooperative nodes J1 , J2 , . . . , JM , and the communication radii R1 , R2 , . . . , RM can be obtained by the approach proposed in [11]. A. Simulation results In this section, we discuss the performance of the proposed scheme in terms of the optimal number of cooperative nodes in each ring, the lifetime of the wireless sensor network, and the available capacity of the sensor nodes. We first describe the simulation setup parameters and then discuss these simulation results. To compare with the peer work [6], we adopt the same sensor deployment scheme and parameter set of communication model as used in that work, shown in Table II. We consider a circular-shape coverage area with 500m radius, divided into 5 rings. Then, we deploy 150 sensor nodes in 5 rings. All sensor nodes are powered by batteries with Model HE18650, which has 3.7-volt nominal voltage, 3-volt cutoff voltage, and 1800mAh nominal capacity. The data of useable capacity vs. voltage are obtained from the Battery Design Studio (BDS) [12] . All parameters of the HE18650 batteries are taken from the built-in model in BDS [12]. The radius, the number of the nodes, and the number of cooperative nodes in each ring are calculated and optimized via MATLAB [13]. The optimal number of cooperative nodes in each ring is listed in Table III, which varies along with the change of communication radius. Therefore, the obtained diversity gain will offset the adverse impact of channel fading and reduce the transmit energy as well as the difference of energy consumption among sensor nodes. The comparison of normalized available capacity and lifetime is shown in Figure 4. Here, the available capacity and
Sequence No. of Rings 1st 2nd 3rd 4th 5th
Optimal No. of Cooperative Nodes 1 2 3 3 4
lifetime of the sensor network with cooperative transmission is normalized to 1. Compared with the scheme without cooperative transmission, the available capacity of the proposed scheme has been enhanced by 52.1%, and the lifetime of cooperative communication has been increased by three times. Therefore, the cooperative transmission can significantly reduce the current discharge of sensor nodes, which consequently enhance the available capacity and lifetime of the sensor networks. The communication radius of each ring derived by using both schemes is plotted in Figure 5, where we can observe that the communication radius of each ring derived from both schemes has been increased from the innermost ring to the outermost ring to achieve the optimal tradeoff between the power consumption and the transmission and communication
1 Non−cooperative Scheme Cooperative Scheme
0.9 0.8 Normalized Available Capacity
2M
Value 500m 0.01 0.95 3volts
TABLE III T HE O PTIMAL N O . OF C OOPERATIVE N O . IN E ACH R ING
The formulated problem can then be solved as a constraint nonlinear programming problem: L(R, N, J, λ) = L1 +
Parameter Name coverage radius connectivity bound the efficiency of the DC-DC output voltage of the DC-DC
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
Fig. 4.
0
0.2
0.4 0.6 Normalized Time
0.8
1
Normalized available capacity vs. normalized time in both schemes
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offsets the adverse impact of channel fading, reduces the transmit energy, and thus saves more power for data communication. To compensate the unbalanced energy consumption caused by saved energy, more sensor nodes are deployed in the innermost ring. Thus, the lifetime of the wireless sensor is prolonged.
200
Communication Radius (m)
Non−cooperative Scheme Cooperative Scheme 150
V. C ONCLUSION 100
50
0 0
1
2 3 4 Sequence Number of Rings
5
6
Fig. 5. The communication radius of each ring, cooperative transmission vs. non-cooperative transmission
Number of Nodes in Each Ring
Non−cooperative Scheme Cooperative Scheme
R EFERENCES
35 30 25 20 15 10 5 0 0
VI. ACKNOWLEDGEMENTS This research was supported in part by NSF ECCS grant no. 0801736.
45 40
In this paper, we have introduced the concept of cooperative transmission into the sensor deployment to prolong the network lifetime. We have showed that the cooperative transmission can significantly reduce the power consumption of sensor nodes. Therefore, more battery energy can be saved for balancing the uneven communication load in the network, leading to a longer lifetime of a given wireless sensor network. Compared with its non-cooperative counterpart, the proposed scheme can improve the available battery capacity by 52.1% as well as prolong the network lifetime by three times.
1
2 3 4 Sequence Number of Rings
5
6
Fig. 6. The number of nodes in each ring, cooperative transmission vs. non-cooperative transmission
load. By adopting cooperative transmission, different numbers of cooperative nodes are assigned to minimize the power consumption of each node, leading to reduce the power consumption for transmission and save power on wireless communication. Recall that the increased average communication load will cause the node in the innermost ring running out of battery more quickly. Therefore, a shorter communication radius is assigned to the sensor nodes residing in the innermost ring, which, in turn, prolong the lifetime of the entire network. The numbers of sensor nodes in each ring by using cooperative transmission and non-cooperative transmission, respectively, are shown in Figure 6. Since the non-cooperative transmission involves more energy consumption to compact wireless communication fading, the energy for communication load is reduced. On the other hand, cooperative transmission
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